A psychoanalyst walks into a bar with a book on logic and set theory. He orders a whisky. And another. Twelve hours and a lock-in later, all he has to show for the evening is a throbbing headache and some indecipherable rubbish scrawled on a napkin.

That’s the only conceivable explanation for these diagrams from *The Subversion of the Subject and the Dialectic of Desire in the Freudian Unconscious*, by Jacques Lacan (published in the *Écrits* collection):

But, surely this notation means something? After all, Lacan is famous and academics across the world dedicate their lives to understanding his genius.

Also the notation *f*(*x*) is a function, *f*, applied to argument *x* – that’s recognisable from maths. So the I(A) and s(A) must mean something…?

To illustrate how function notation is usually used, consider the Fibonacci sequence, which pops up in all kinds of interesting places in nature. It is defined as follows:

*f*(0) = 0,

*f*(1) = 1,

*f*(*n*) = *f*(*n*-1) + *f*(*n*-2), for *n* > 1.

In English, this says that the first two numbers in the sequence are 0 and 1 and the numbers following are obtained by summing the previous two. So the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

The function notation “does something”. It provides a way of defining and referring to (here, mathematical) concepts. I claim that the brief explanation above would make some kind of sense to most people who can add two numbers together.

Less well-known, but appearing in university philosophy courses, is the lozenge symbol, ◊, which means “possible” in a particular kind of logic called modal logic. So if *R* stands for “it’s raining” then ◊*R* stands for “it’s possible that it’s raining”. It seems plausible that there is something meaningful here in Lacan’s use of the symbol too.

Here is Lacan, “explaining” his notation to his almost entirely non-mathematical readership:

Huh?

Lacan doesn’t try to explain what the notation means; he doesn’t seem to want readers to understand. Maybe he is just too clever and if only we persevered we would get what he means. Elsewhere in the same text, Lacan uses arithmetic to argue that “the erectile organ can be equated with \(\sqrt{-1}\)”. I’m told this is a joke because \(\sqrt{-1}\) is an imaginary number. Maybe trainee psychoanalysts learn about complex numbers so get the joke. I doubt it though. Maybe all Lacanian discourse is dadaist performance – that at least would make some sense.

Alan Sokal and Jean Bricmont have written a book-length critique of Lacan’s maths and others’ similar use of natural science concepts. Having read lots of mathematical texts and seen how authors make an effort to introduce their notation, I think it’s entirely possible Lacan is a fraud, ◊(Lacan is a fraud). That might sound harsh, but forget how famous he is and just look at the pretentious rubbish he writes.